Lecture Notes in Advanced Thermodynamics

2.1.1 Basic notations
basic state variables: (E, V, M) ∈ (R + ) 3
(they can be chosen intuitively or considering physical meaning)
state function: an f(E, V, M) : (R + ) 3 → R function which creates a new
state variable from the basic state variables
extensive scaling of a state function (f◦λ)(E, V, M) := f(λE, λV, λM),
where λ is an arbitrary real number
(resizes the system, giving the value of the state function for a λ times
,,larger” body )
intensive state function: f ◦ λ = f for ∀λ ∈ R
(the state function remains constant if the body is resized)
extensive state function: f ◦ λ = λ · f for ∀λ ∈ R
(the state function is increasing linearly with the resizing)
remarks:
– the function itself and the value of the function are not strictly distinguished
in notation
– in the definitions and following calculations equal sign (=) between
state functions means equality for all possible (E, V, M) values
– E, V and M can be considered also as extensive state functions, e.g.
E(E, V, M) = E
– the partial derivation of a function can be denoted in shorter way:
∂f(E, V, M) ∂f
=:
∂E ∂E ∣ =: ∂ E f
V,M
2.1.2 Definition of the model
Definition(discrete thermostatic body):
– a set of ⎧ ⎫
⎨ T (E, V, M) ⎬
p(E, V, M)
⎩ ⎭
µ(E, V, M)
state functions over the (E, V, M) state space
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